6 papers · 1 filter
The doubling property of the elliptic measure, for elliptic operators with drifts satisfying an average diverging condition
Aritro Pathak
We show doubling of the elliptic measure corresponding to the operator with an elliptic principal term and a drift that diverges, on average on Whitney cubes, like the inverse dist…
Dirichlet Green's functions with singular drifts at the boundary of convex domains
Aritro Pathak
In convex bounded domains in R^n with n >= 3, we establish interior pointwise upper bounds for the Dirichlet Green's function of elliptic operators in the unit ball B(0,1) in R^n,…
Pointwise bounds on Dirichlet Green's functions for a singular drift term
Aritro Pathak
We introduce a technique to obtain pointwise upper and lower bounds for the Green's function of elliptic operators whose principal part is the Laplacian and that include a drift te…
On the dimension drop for harmonic measure on uniformly non-flat Ahlfors-David regular boundaries
Aritro Pathak
We extend earlier results of Azzam on the dimension drop of the harmonic measure for a domain with , with dimensional Ahlfors regular boundary $\partial…
A counterexample for pointwise upper bounds on Green's function with a singular drift at boundary
Aritro Pathak
We show an example of a sequence of elliptic operators in the unit ball with drifts that diverge as the inverse distance to the boundary, for which we do not get uniform upper esti…
BMO solvability with singular drifts on ample sawtooth domains implies solvability
Aritro Pathak
For a linear elliptic operator with a singular drift that satisfies a finite Carleson measure condition, we prove that there exist `ample' sawtooth domains of the unit ball $B(0,1)…